Common Core Learning Standard
Students will use their understanding of and skill with multiplication, division and fractions as they study ratios, rates and proportional relationships by viewing equivalent ratios and rates as derivations or extensions of pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities. Students use a range of reasoning and representations to analyze proportional relationships. Their work in this unit will link with work in representing relationships between independent and dependent variables as well as setting the foundation for 8th grade work with linear equations. The Mathematical Practices should be evident throughout instruction and connected to the content addressed in this unit. Students should engage in mathematical tasks that provide an opportunity to connect content and practices.
Big Idea Students use reasoning about multiplication and division to solve ratio and rate problems about quantities.
Essential Questions:
What is the connection between a ratio and a fraction?
Why is it important to know how to solve for unit rates?
How is a ratio or rate used to compare two quantities or values?
How and where are ratios and rates used in the real world?
How can I model and represent rates and ratios?
What are similarities and differences between fractions and ratios?
Vocabulary
Percent: A fraction or ration in which the denominator is 100
Proportion: An equation which states that two ratios are equal.
Rate: A comparison of two quantities that have different units of measure
Ratio: compares quantities that share a fixed, multiplicative relationship.
Rational number: A number that can be written as a/b where a and b are integers, but b is not equal to 0.
Unit Rate: are ratios written as some number to 1.
Quantity: is an amount that can be counted or measured.
Content
gain a deeper understanding of proportional reasoning through instruction and practice will develop and use multiplicative thinking
develop a sense of proportional reasoning
develop the understanding that ratio is a comparison of two numbers or quantities
find percents using the same processes for solving rates and proportions
solve real-life problems involving measurement units that need to be converted
Skills Needed
Multiples and Factors
Divisibility Rules
Relationships and rules for multiplication and division of whole numbers as they apply to
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there
was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
6.RP.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the
context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there
is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
(Expectations for unit rates in this grade are limited to non-complex fractions).
6.RP.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of
equivalent ratios, tape diagrams, double number line diagrams, or equations.
6.RP.3a
Make tables of equivalent ratios relating quantities with whole- number measurements, find missing values in the
tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
6.RP.3b
Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours
to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being
mowed?
6.RP.3c
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve
problems involving finding the whole, given a part and the percent.
Table of Contents
Common Core Learning Standard
Students will use their understanding of and skill with multiplication, division and fractions as they study ratios, rates and proportional relationships by viewing equivalent ratios and rates as derivations or extensions of pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities. Students use a range of reasoning and representations to analyze proportional relationships. Their work in this unit will link with work in representing relationships between independent and dependent variables as well as setting the foundation for 8th grade work with linear equations. The Mathematical Practices should be evident throughout instruction and connected to the content addressed in this unit. Students should engage in mathematical tasks that provide an opportunity to connect content and practices.
Big Idea
Students use reasoning about multiplication and division to solve ratio and rate problems about quantities.
Essential Questions:
Vocabulary
Content
Skills Needed
Arc 1 - Ratios
HW
Pearson All-in-One Workbook Version A
P333. Q1-15
workbook
Brain Pop Ratios
Math Playground Ratio
Math Playground Equal Ratis
Math Playground Solving RatioWord Problems
Math Playground More Ratio
IXL Describe Ratio Pictures
HW
Pearson All-in-One Workbook Version A
P333. Q1-15. Write in words.
(ex - for every 1 cow, there are 4 chickens)
workbook
HW
Pearson All-in-One Workbook Version A
P339. Q7-14
workbook
Math Playground Proportions
IXL Proportions
HW
Pearson All-in-One Workbook Version A
p339. Q15-19
workbook
HW
workbook
Dirt Bike Ratios
HW
workbook
IXL Ratio Tables
Math Connects
HW
Recommends
Lesson
CC-7
HW
workbook
Math Connects
HW
workbook
Brain Pop Linear Equations
HW
workbook
Individual Practice
HW
Arc 2 - Rate
HW
Pearson All-in-One Workbook Version A
P271. Q12-19.
Change each fraction into a RATE.
workbook
(what is x% of y)
HW
Pearson All-in-One Workbook Version A
P345. Q1-15
workbook
IXL Find Percentage
(x is what % of y)
HW
workbook
IXL Find Percent
IXL Percent Word Problems
HW
Pearson All-in-One Workbook Version A
P335. Q1-6.
workbook
IXL Unit Rates
IXL Unit Rate Word Problems
HW
Pearson All-in-One Workbook Version A
P335. Q13-18.
workbook
Motivation Video
HW
workbook
Individual Practice
HW
Unit Assessments
&
Post-Assessment
Standards
For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there
was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there
is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
(Expectations for unit rates in this grade are limited to non-complex fractions).
equivalent ratios, tape diagrams, double number line diagrams, or equations.
tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being
mowed?
problems involving finding the whole, given a part and the percent.